Question

The point $(a,2a)$ is an interior point of the region bounded by the parabola $y^2=16x$ and the double ordinate through the focus. Then $a$ belongs to open interval

• A. $a<4$
• B. $0<a<4$
• C. $0<a<2$
• D. $a>4$

Answer 1

The correct option is B $0<a<4$

For $(a,2a)$ to be interior point of parabola $y^2=16x$
$(2a{)}^2-16(a)<0\Rightarrow a^2-4a<0\Rightarrow a(a-4)<0\Rightarrow aϵ(0,4)$
Now double ordinate through focus is $x=4$
Using other given condition $a<4$
Hence, acceptable range of $a$ is $(0,4)$